2-power domination number for Knödel graphs and its application in communication networks

• Published in: R.A.I.R.O. Recherche opérationnelle Vol. 57; no. 6; pp. 3157 - 3168
• Main Authors: Sundara Rajan, R., Arulanand, S., Prabhu, S., Rajasingh, Indra
• Format: Journal Article
• Language: English
• Published: 01.11.2023
• ISSN: 0399-0559; 2804-7303
• DOI: 10.1051/ro/2023173

In a graph G , if each node v  ∈  V ( G ) \  S is connected to some node in S , then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ ( G ). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G . The power domination number of G is the least number of vertices of a power dominating set of G . A generalization of power domination is the k -power domination in a graph G . The k -power domination number of G is the minimum cardinality of all k -power dominating sets of G and is represented by γ p , k (G). In this paper, we have obtained the 2-power domination number represented by γ p ,2 (G) for 4-regular Knödel graphs and given the lower bound for 5-regular Knödel graphs.